Der a-te Teil eines Terms, addiert zum b-ten Teil desselben Terms, gibt die doppelte Summe von a und b. Wie heisst der Term?

Hallo Anonymous,

hier die Übersetzung in die mathematische Sprache:

$${\frac{{\mathtt{1}}}{{\mathtt{a}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{b}}}} = {\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}\right)$$

kann man noch umformen  =>     2ab = 1

$${\frac{{\mathtt{b}}}{{\mathtt{ab}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{a}}}{{\mathtt{ab}}}} = {\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}\right)$$     =>   $${\frac{\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}\right)}{{\mathtt{ab}}}} = {\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}\right)$$   =>   $${\frac{\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}\right)}{\left(\left({\mathtt{a}}{\mathtt{\,\small\textbf+\,}}{\mathtt{b}}\right){\mathtt{\,\times\,}}{\mathtt{ab}}\right)}} = {\mathtt{2}}$$

$${\frac{{\mathtt{1}}}{{\mathtt{ab}}}} = {\mathtt{2}}$$    =>     2ab = 1           =>     a*b = 0,5       =>    a = 0,5 / b

Gruß radix !